Example of Computation of inverse Fourier transform (CT signals)
A practice problem on CT Fourier transform
$ X(\omega) = \frac{j\omega}{7 + j\omega} $
$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty}\frac{j\omega e^{j\omega t}}{7 + j\omega}d\omega $
$ = \frac{j\omega}{2\pi} \int_{-\infty}^{\infty}\frac{e^{j\omega t}}{7 + j\omega}d\omega $
$ = \frac{d}{dt}e^{-7t}u(t) $
